Revision 04bbc417cf2927b827660bc07743429783569aec authored by HwB on 10 February 2013, 00:00:00 UTC, committed by Gabor Csardi on 10 February 2013, 00:00:00 UTC
1 parent 0e3ae6b
bisect.R
##
## b i s e c t . R
##
bisect <- function(f, a, b, maxiter=100, tol=.Machine$double.eps^0.5)
# Bisection search for zero of a univariate function in a bounded interval
{
if (f(a)*f(b) > 0) stop("f(a) and f(b) must have different signs.")
x1 <- min(a, b); x2 <- max(a,b)
xm <- (x1+x2)/2.0
n <- 0
while (abs(x1-x2)/2.0 > tol) {
n <- n+1
if (abs(f(xm)) <= tol) break
if (f(x1)*f(xm) < 0) {
x2 <- xm
} else {
x1 <- xm
}
xm <- (x1+x2)/2.0 # xm <- x1 - f(x1) * (x2-x1) / (f(x2)-f(x1))
if (n >= maxiter) break
}
return(list(root=xm, f.root=f(xm), iter=n, estim.prec=abs(x1-x2)/2.0))
}
regulaFalsi <- function(f, a, b, maxiter=100, tol=.Machine$double.eps^0.5)
#Regula Falsi search for zero of a univariate function in a bounded interval
{
x1 <- a; x2 <- b
f1 <- f(x1); f2 <- f(x2)
if (f1*f2 > 0) stop("f(a) and f(b) must have different signs.")
m <- 0.5 # Illinois rule
niter <- 0
while (abs(x2-x1) >= tol && niter <= maxiter) {
niter <- niter + 1
x3 <- (x1*f2-x2*f1)/(f2-f1); f3 <- f(x3)
if(f3*f2 < 0) {
x1 <- x2; f1 <- f2
x2 <- x3; f2 <- f3
} else {
# m <- f2/(f2+f3) # Pegasus rule
# m <- if (1-f3/f2 > 0) 1-f3/f2 else 0.5 # Andersen/Bjoerk
f1 <- m * f1
x2 <- x3; f2 <- f3
}
}
if (niter > maxiter && abs(x2-x1) >= tol)
cat("regulaFalsi stopped without converging.\n")
return(list(root = x3, f.root = f3, niter = niter, estim.prec = x1-x2))
}
secant <- function(fun, a, b, ...,
maxiter = 100, tol = .Machine$double.eps^0.5)
# Secant search for zero of a univariate function
{
fun <- match.fun(fun)
f <- function(x) fun(x, ...)
x1 <- a; x2 <- b
f1 <- f(x1); if (abs(f1) <= tol) return(x1)
f2 <- f(x2); if (abs(f2) <= tol) return(x1)
n <- 0
while (n <= maxiter && abs(x2 - x1) > tol) {
n <- n+1
slope <- (f2 - f1)/(x2 - x1)
if (slope == 0) return(root=NA, f.root=NA, iter=n, estim.prec=NA)
x3 <- x2 - f2/slope
f3 <- f(x3); if (abs(f3) <= tol) break
x1 <- x2; f1 <- f2
x2 <- x3; f2 <- f3
}
if (n > maxiter) {
warning("Maximum number of iterations 'maxiter' was reached.")
}
return(list(root=x3, f.root=f3, iter=n, estim.prec=2*abs(x3-x2)))
}
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